{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RFXS5R3ZVIWUDZDFA26AU3QOEZ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"97435f17ef223336f488fdbb99fc5ae846ad15f771734370e6f0673823db3392","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-09-23T20:52:21Z","title_canon_sha256":"abe598a195cad90b9f51643529f158b902aa9fc7814126e3e394e02eeea36db1"},"schema_version":"1.0","source":{"id":"1109.5198","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5198","created_at":"2026-05-18T00:17:24Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5198v2","created_at":"2026-05-18T00:17:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5198","created_at":"2026-05-18T00:17:24Z"},{"alias_kind":"pith_short_12","alias_value":"RFXS5R3ZVIWU","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RFXS5R3ZVIWUDZDF","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RFXS5R3Z","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:b269f1ebe1140e79996193e0aaf77d80531094b0eda49abd6205adcceae27df2","target":"graph","created_at":"2026-05-18T00:17:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We give a complete description of the cone of Betti diagrams over a standard graded hypersurface ring of the form k[x,y]/<q>, where q is a homogeneous quadric. We also provide a finite algorithm for decomposing Betti diagrams, including diagrams of infinite projective dimension, into pure diagrams. Boij--Soederberg theory completely describes the cone of Betti diagrams over a standard graded polynomial ring; our result provides the first example of another graded ring for which the cone of Betti diagrams is entirely understood.","authors_text":"Christine Berkesch, Courtney Gibbons, Daniel Erman, Jesse Burke","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-09-23T20:52:21Z","title":"The cone of Betti diagrams over a hypersurface ring of low embedding dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5198","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:377d986bdd9fc2e092c0cf9eccacc7fce19d8e716b64f770858ae05e2356ceab","target":"record","created_at":"2026-05-18T00:17:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"97435f17ef223336f488fdbb99fc5ae846ad15f771734370e6f0673823db3392","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-09-23T20:52:21Z","title_canon_sha256":"abe598a195cad90b9f51643529f158b902aa9fc7814126e3e394e02eeea36db1"},"schema_version":"1.0","source":{"id":"1109.5198","kind":"arxiv","version":2}},"canonical_sha256":"896f2ec779aa2d41e46506bc0a6e0e26597fe27b715a774e592612c36e418a8c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"896f2ec779aa2d41e46506bc0a6e0e26597fe27b715a774e592612c36e418a8c","first_computed_at":"2026-05-18T00:17:24.803532Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:24.803532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8PvMjPtO3F1ZLZibsr7fxpgy2i3z+i+15vxL4vIWBtky5l52oTnR+D0O4N/EOoyVbCVdZ4ytApgdixS1uy5wCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:24.804067Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5198","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:377d986bdd9fc2e092c0cf9eccacc7fce19d8e716b64f770858ae05e2356ceab","sha256:b269f1ebe1140e79996193e0aaf77d80531094b0eda49abd6205adcceae27df2"],"state_sha256":"eef0c9584af6bb57c3dcddd98267e8c4621e3b745f149545cbc5ff7a68f8579c"}